Analyses will be conducted in R. All observations from 2010-2013 were removed from analysis due to changes in reporting calculated scores. An additional 33 records with missing values were excluded from overall analysis. Summary statistics for each calculated score will be reviewed, including: number of readmissions, readmission rate, odds of readmission, and log odds. Covariates will be reviewed for sufficient sample size within each group to include in model-fitting. Exploratory data analysis will also include visualizations of empirical log odds (logits) for each calculated score across all potential covariates.
Model fitting will begin with logistic regression considering the association of acuity score with readmission risk. Separate models will be fitted for each acuity score, and expand to consider covariates as appropriate. Additional observations may be dropped or aggregated in consideration of sample size and will be noted in each case. Individual models will be assessed through reviewing deviance residuals and conducting a \(\chi^2\) goodness-of-fit test. Individual predictors will be assessed with confidence intervals. Models will be compared using Akaike’s Information Criteria.
Note: add a MC simulation if there’s enough time!
Our primary research interest is whether or not the probability of readmission is associated with calculated score. We calculate the odds \(\frac{p}{1-p}\) empirical log odds \(log(\frac{p}{1-p})\) of readmissions associated with each level of each acuity score and visualize the potential associations, where \(p\) is the probability that a record is of a readmission within 30 days. Summary tables for CCI, LACE, and HOSPITAL can be found in Appendix A: .
A linear association between CCI score and empirical logit is not clear, especially considering score values greater than 8. A linear association between HOSPITAL score and empirical logit is quite pronounced; while the linear association between LACE score and empirical logit is also quite strong, we can observe two potential outliers for LACE score values of 3 and 18.
We also want to consider whether or not probability of readmission changes over time, with respect to acuity score. Various plots examining readmission by score over year can be found in Appendix B; no interaction between score and year is apparent.
We are also interested in the potential effect demographic factors have on the relationship between readmission rate and acuity score. Due to the small sample sizes from considering multiple demographics together, we will disaggregate readmission by each acuity score over one demographic factor (Gender, Race/Ethnicity, Insurance) at a time. Tables and plots for readmission logits by demographic covariates are available in Appendix C. Sample sizes among groups for Race/Ethnicity are too small for this factor to be considered in model fitting; however, previous analysis showed strong evidence that Race/Ethnicity was associated with differences in calculated scores while controlling for other factors. Consequently, this factor should be examined in further study of readmission rates.
Logistic regression is the appropriate model class for our binary response, where we want to model the probability that a record is for a readmission within 30 days. CCI values ranged 0-15; score values of 16, 17 were excluded due to small sample size (n = 1). LACE values ranged 2-19; no values were excluded. HOSPITAL values ranged 0-11; score values of 12 were excluded due to small sample size (n = 2). We start model fitting with a basic model for each calculated score.
The base model for readmission against CCI can be written as:
\[ \begin{aligned} log(\frac{p_{CCI_i}}{1-p_{CCI_{i}}}) &= \beta_0 + \beta_1 CCI_i \\ p_{CCI_{i}} &= \frac{e^{\beta_0 + \beta_1CCI_{i}}}{1 + e^{\beta_0 + \beta_1CCI_{i}}} \end{aligned} \] where \(i\ \epsilon\ [0, 14]\)
The estimated odds ratio for CCI is \(e^{\hat{B_1}} = e^{0.003} = 1.003\), 95% CI: (0.98, 1.03); we find no evidence that CCI score is associated with risk for readmission within 30 days.
The estimated model for probability of readmission can be estimated as:
\[p_{CCI_i} = \frac{e^{-1.701 + 0.003*CCI_i}}{1+e^{-1.701 + 0.003*CCI_i}}\]
Note: Add manual legend! The line is the fitted model line, and the blue squares are the fitted values. The red circles are the empirical proportions of readmissions for each value of CCI. The black blobs are the raw data for each record. Maybe remove this last piece, since it doesn’t add much to the visual story
Full model diagnostics can be reviewed in Appendix D. No CCI + covariate models need to be fitted since we find no evidence that changes in CCI score are associated with changes in readmission risk.
The base model for readmission against LACE can be written as:
\[ \begin{aligned} log(\frac{p_{LACE_i}}{1-p_{LACE_{i}}}) &= \beta_0 + \beta_1 LACE_i \\ p_{LACE_{i}} &= \frac{e^{\beta_0 + \beta_1LACE_{i}}}{1 + e^{\beta_0 + \beta_1LACE_{i}}} \end{aligned} \] where \(i\ \epsilon\ [2, 19]\)
The estimated odds ratio for LACE is \(e^{\hat{B_1}} = e^{0.155} = 1.167\), 95% CI: (1.117, 1.221); these results provide evidence that odds of readmission increases 11.7% - 22.1% for each increased value in LACE score. The confidence intervals given are calculated with an quasibinomial overdispersion parameter \(\phi = 4.26\) to account for extra-binomial variation present in the data. See Appendix E for full model diagnostics.
The estimated model for probability of readmission can be estimated as:
\[p_{LACE_i} = \frac{e^{-3.521 + 0.155*LACE_i}}{1+e^{-3.521 + 0.155*LACE_i}}\]
Note: need to plot base model, fit models with covariates, and perform model selection
The base model for readmission against HOSPITAL can be written as:
\[
\begin{aligned}
log(\frac{p_{HOS_i}}{1-p_{HOS_{i}}}) &= \beta_0 + \beta_1 HOS_i \\
p_{HOS_{i}} &= \frac{e^{\beta_0 + \beta_1HOS_{i}}}{1 + e^{\beta_0 + \beta_1HOS_{i}}}
\end{aligned}
\]
where \(i\ \epsilon\ [0, 11]\)
The estimated odds ratio readmission risk for HOSPITAL is \(e^{\hat{B_1}} = e^{0.251} = 1.285\), 95% CI: (1.253, 1.318); these results provide evidence that odds of readmission increases between 25.3% - 31.8% for each increased value in HOSPITAL score.
The estimated model for probability of readmission can be estimated as:
\[p_{HOSP_i} = \frac{e^{-2.708 + 0.251*HOSP_i}}{1+e^{-2.708 + 0.251*HOSP_i}}\]
Full model diagnostics are available in Appendix F
Note need to plot base model, fit models with covariates, and perform model selection
Note: will add more based on discussion and additional model fitting
| CCI Score | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|
| 0 | 41.634 | 71 | 10 | 0.141 | 0.164 | -1.808 |
| 1 | 53.778 | 243 | 28 | 0.115 | 0.130 | -2.038 |
| 2 | 63.191 | 876 | 130 | 0.148 | 0.174 | -1.747 |
| 3 | 71.419 | 1948 | 301 | 0.155 | 0.183 | -1.700 |
| 4 | 82.571 | 4049 | 641 | 0.158 | 0.188 | -1.671 |
| 5 | 81.987 | 2638 | 427 | 0.162 | 0.193 | -1.644 |
| 6 | 83.461 | 1842 | 300 | 0.163 | 0.195 | -1.637 |
| 7 | 84.144 | 999 | 141 | 0.141 | 0.164 | -1.806 |
| 8 | 83.855 | 517 | 90 | 0.174 | 0.211 | -1.557 |
| 9 | 83.144 | 250 | 33 | 0.132 | 0.152 | -1.883 |
| 10 | 82.527 | 148 | 21 | 0.142 | 0.165 | -1.800 |
| 11 | 79.387 | 75 | 9 | 0.120 | 0.136 | -1.992 |
| 12 | 82.533 | 92 | 13 | 0.141 | 0.165 | -1.804 |
| 13 | 84.294 | 34 | 11 | 0.324 | 0.478 | -0.738 |
| 14 | 84.632 | 19 | 0 | 0.000 | 0.000 | -Inf |
| 15 | 84.857 | 7 | 0 | 0.000 | 0.000 | -Inf |
| 16 | 79.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| 17 | 83.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| LACE Score | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|
| 2 | 42.400 | 5 | 0 | 0.000 | 0.000 | -Inf |
| 3 | 48.200 | 5 | 1 | 0.200 | 0.250 | -1.386 |
| 4 | 57.273 | 44 | 1 | 0.023 | 0.023 | -3.761 |
| 5 | 61.650 | 100 | 5 | 0.050 | 0.053 | -2.944 |
| 6 | 67.569 | 239 | 17 | 0.071 | 0.077 | -2.569 |
| 7 | 69.838 | 359 | 44 | 0.123 | 0.140 | -1.968 |
| 8 | 75.058 | 652 | 76 | 0.117 | 0.132 | -2.025 |
| 9 | 77.822 | 1115 | 129 | 0.116 | 0.131 | -2.034 |
| 10 | 77.225 | 1462 | 210 | 0.144 | 0.168 | -1.785 |
| 11 | 78.390 | 1683 | 203 | 0.121 | 0.137 | -1.987 |
| 12 | 82.185 | 3043 | 402 | 0.132 | 0.152 | -1.882 |
| 13 | 81.588 | 2997 | 517 | 0.173 | 0.208 | -1.568 |
| 14 | 80.683 | 596 | 131 | 0.220 | 0.282 | -1.267 |
| 15 | 79.825 | 1203 | 313 | 0.260 | 0.352 | -1.045 |
| 16 | 80.017 | 234 | 80 | 0.342 | 0.519 | -0.655 |
| 17 | 77.377 | 53 | 21 | 0.396 | 0.656 | -0.421 |
| 18 | 78.273 | 11 | 1 | 0.091 | 0.100 | -2.303 |
| 19 | 81.111 | 9 | 4 | 0.444 | 0.800 | -0.223 |
| HOS Score | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|
| 0 | 79.000 | 86 | 3 | 0.035 | 0.036 | -3.320 |
| 1 | 78.553 | 1198 | 80 | 0.067 | 0.072 | -2.637 |
| 2 | 79.491 | 2045 | 170 | 0.083 | 0.091 | -2.401 |
| 3 | 79.933 | 2578 | 378 | 0.147 | 0.172 | -1.761 |
| 4 | 80.051 | 3934 | 598 | 0.152 | 0.179 | -1.719 |
| 5 | 78.902 | 1585 | 310 | 0.196 | 0.243 | -1.414 |
| 6 | 78.322 | 1532 | 357 | 0.233 | 0.304 | -1.191 |
| 7 | 77.354 | 390 | 104 | 0.267 | 0.364 | -1.012 |
| 8 | 75.410 | 288 | 92 | 0.319 | 0.469 | -0.756 |
| 9 | 72.976 | 124 | 47 | 0.379 | 0.610 | -0.494 |
| 10 | 71.750 | 28 | 9 | 0.321 | 0.474 | -0.747 |
| 11 | 71.950 | 20 | 7 | 0.350 | 0.538 | -0.619 |
| 12 | 82.500 | 2 | 0 | 0.000 | 0.000 | -Inf |
| CCI Score | Gender | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|---|
| 0 | Female | 42.651 | 43 | 5 | 0.116 | 0.132 | -2.028 |
| Male | 40.071 | 28 | 5 | 0.179 | 0.217 | -1.526 | |
| 1 | Female | 54.348 | 141 | 18 | 0.128 | 0.146 | -1.922 |
| Male | 52.990 | 102 | 10 | 0.098 | 0.109 | -2.219 | |
| 2 | Female | 63.377 | 525 | 68 | 0.130 | 0.149 | -1.905 |
| Male | 62.912 | 351 | 62 | 0.177 | 0.215 | -1.539 | |
| 3 | Female | 71.620 | 1188 | 165 | 0.139 | 0.161 | -1.825 |
| Male | 71.104 | 760 | 136 | 0.179 | 0.218 | -1.523 | |
| 4 | Female | 83.058 | 2567 | 352 | 0.137 | 0.159 | -1.839 |
| Male | 81.728 | 1482 | 289 | 0.195 | 0.242 | -1.418 | |
| 5 | Female | 82.344 | 1665 | 232 | 0.139 | 0.162 | -1.821 |
| Male | 81.376 | 973 | 195 | 0.200 | 0.251 | -1.384 | |
| 6 | Female | 83.712 | 1167 | 162 | 0.139 | 0.161 | -1.825 |
| Male | 83.028 | 675 | 138 | 0.204 | 0.257 | -1.359 | |
| 7 | Female | 84.626 | 626 | 78 | 0.125 | 0.142 | -1.950 |
| Male | 83.335 | 373 | 63 | 0.169 | 0.203 | -1.593 | |
| 8 | Female | 84.205 | 317 | 53 | 0.167 | 0.201 | -1.606 |
| Male | 83.300 | 200 | 37 | 0.185 | 0.227 | -1.483 | |
| 9 | Female | 83.339 | 168 | 23 | 0.137 | 0.159 | -1.841 |
| Male | 82.744 | 82 | 10 | 0.122 | 0.139 | -1.974 | |
| 10 | Female | 83.012 | 84 | 6 | 0.071 | 0.077 | -2.565 |
| Male | 81.891 | 64 | 15 | 0.234 | 0.306 | -1.184 | |
| 11 | Female | 79.604 | 48 | 6 | 0.125 | 0.143 | -1.946 |
| Male | 79.000 | 27 | 3 | 0.111 | 0.125 | -2.079 | |
| 12 | Female | 82.621 | 58 | 8 | 0.138 | 0.160 | -1.833 |
| Male | 82.382 | 34 | 5 | 0.147 | 0.172 | -1.758 | |
| 13 | Female | 85.957 | 23 | 8 | 0.348 | 0.533 | -0.629 |
| Male | 80.818 | 11 | 3 | 0.273 | 0.375 | -0.981 | |
| 14 | Female | 84.833 | 12 | 0 | 0.000 | 0.000 | -Inf |
| Male | 84.286 | 7 | 0 | 0.000 | 0.000 | -Inf | |
| 15 | Female | 83.333 | 6 | 0 | 0.000 | 0.000 | -Inf |
| Male | 94.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| 16 | Male | 79.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| 17 | Female | 83.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| CCI Score | Race/Ethnicity | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|---|
| 0 | African Amer/Black | 42.160 | 25 | 5 | 0.200 | 0.250 | -1.386 |
| Asian | 37.857 | 7 | 1 | 0.143 | 0.167 | -1.792 | |
| Caucasian/White | 43.231 | 26 | 4 | 0.154 | 0.182 | -1.705 | |
| Hispanic/Latino | 41.714 | 7 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 36.833 | 6 | 0 | 0.000 | 0.000 | -Inf | |
| 1 | African Amer/Black | 52.292 | 65 | 13 | 0.200 | 0.250 | -1.386 |
| Asian | 56.444 | 9 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 54.760 | 125 | 12 | 0.096 | 0.106 | -2.242 | |
| Hispanic/Latino | 51.706 | 17 | 2 | 0.118 | 0.133 | -2.015 | |
| Other/Multiracial | 53.105 | 19 | 1 | 0.053 | 0.056 | -2.890 | |
| Unavailable/Unknown | 53.500 | 8 | 0 | 0.000 | 0.000 | -Inf | |
| 2 | African Amer/Black | 61.280 | 164 | 31 | 0.189 | 0.233 | -1.456 |
| Asian | 63.739 | 46 | 7 | 0.152 | 0.179 | -1.718 | |
| Caucasian/White | 63.742 | 565 | 77 | 0.136 | 0.158 | -1.847 | |
| Hispanic/Latino | 62.000 | 43 | 6 | 0.140 | 0.162 | -1.819 | |
| Other/Multiracial | 63.833 | 48 | 7 | 0.146 | 0.171 | -1.768 | |
| Unavailable/Unknown | 62.900 | 10 | 2 | 0.200 | 0.250 | -1.386 | |
| 3 | African Amer/Black | 69.118 | 296 | 47 | 0.159 | 0.189 | -1.667 |
| Asian | 71.280 | 125 | 21 | 0.168 | 0.202 | -1.600 | |
| Caucasian/White | 72.124 | 1287 | 204 | 0.159 | 0.188 | -1.669 | |
| Hispanic/Latino | 69.622 | 82 | 9 | 0.110 | 0.123 | -2.093 | |
| Other/Multiracial | 70.135 | 111 | 10 | 0.090 | 0.099 | -2.313 | |
| Unavailable/Unknown | 73.149 | 47 | 10 | 0.213 | 0.270 | -1.308 | |
| 4 | African Amer/Black | 77.255 | 404 | 74 | 0.183 | 0.224 | -1.495 |
| Asian | 79.578 | 128 | 14 | 0.109 | 0.123 | -2.097 | |
| Caucasian/White | 83.588 | 3133 | 497 | 0.159 | 0.189 | -1.668 | |
| Hispanic/Latino | 79.292 | 120 | 11 | 0.092 | 0.101 | -2.293 | |
| Other/Multiracial | 80.909 | 187 | 33 | 0.176 | 0.214 | -1.540 | |
| Unavailable/Unknown | 83.221 | 77 | 12 | 0.156 | 0.185 | -1.689 | |
| 5 | African Amer/Black | 77.605 | 243 | 43 | 0.177 | 0.215 | -1.537 |
| Asian | 78.714 | 91 | 11 | 0.121 | 0.138 | -1.984 | |
| Caucasian/White | 82.993 | 2034 | 327 | 0.161 | 0.192 | -1.653 | |
| Hispanic/Latino | 79.207 | 92 | 12 | 0.130 | 0.150 | -1.897 | |
| Other/Multiracial | 79.073 | 124 | 19 | 0.153 | 0.181 | -1.710 | |
| Unavailable/Unknown | 80.741 | 54 | 15 | 0.278 | 0.385 | -0.956 | |
| 6 | African Amer/Black | 80.383 | 162 | 24 | 0.148 | 0.174 | -1.749 |
| Asian | 80.385 | 65 | 9 | 0.138 | 0.161 | -1.828 | |
| Caucasian/White | 84.149 | 1454 | 240 | 0.165 | 0.198 | -1.621 | |
| Hispanic/Latino | 78.755 | 53 | 6 | 0.113 | 0.128 | -2.058 | |
| Other/Multiracial | 82.974 | 76 | 12 | 0.158 | 0.188 | -1.674 | |
| Unavailable/Unknown | 83.031 | 32 | 9 | 0.281 | 0.391 | -0.938 | |
| 7 | African Amer/Black | 80.221 | 95 | 13 | 0.137 | 0.159 | -1.842 |
| Asian | 80.571 | 28 | 3 | 0.107 | 0.120 | -2.120 | |
| Caucasian/White | 84.722 | 809 | 120 | 0.148 | 0.174 | -1.748 | |
| Hispanic/Latino | 80.947 | 19 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 87.188 | 32 | 2 | 0.062 | 0.067 | -2.708 | |
| Unavailable/Unknown | 82.188 | 16 | 3 | 0.188 | 0.231 | -1.466 | |
| 8 | African Amer/Black | 79.500 | 50 | 8 | 0.160 | 0.190 | -1.658 |
| Asian | 79.417 | 12 | 2 | 0.167 | 0.200 | -1.609 | |
| Caucasian/White | 84.750 | 412 | 72 | 0.175 | 0.212 | -1.552 | |
| Hispanic/Latino | 84.385 | 13 | 2 | 0.154 | 0.182 | -1.705 | |
| Other/Multiracial | 79.962 | 26 | 6 | 0.231 | 0.300 | -1.204 | |
| Unavailable/Unknown | 83.000 | 4 | 0 | 0.000 | 0.000 | -Inf | |
| 9 | African Amer/Black | 76.522 | 23 | 3 | 0.130 | 0.150 | -1.897 |
| Asian | 72.333 | 6 | 1 | 0.167 | 0.200 | -1.609 | |
| Caucasian/White | 84.710 | 200 | 25 | 0.125 | 0.143 | -1.946 | |
| Hispanic/Latino | 77.778 | 9 | 2 | 0.222 | 0.286 | -1.253 | |
| Other/Multiracial | 79.375 | 8 | 1 | 0.125 | 0.143 | -1.946 | |
| Unavailable/Unknown | 78.750 | 4 | 1 | 0.250 | 0.333 | -1.099 | |
| 10 | African Amer/Black | 76.111 | 9 | 1 | 0.111 | 0.125 | -2.079 |
| Asian | 78.750 | 4 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 83.043 | 115 | 18 | 0.157 | 0.186 | -1.684 | |
| Hispanic/Latino | 81.700 | 10 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 85.375 | 8 | 2 | 0.250 | 0.333 | -1.099 | |
| Unavailable/Unknown | 82.000 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| 11 | African Amer/Black | 79.182 | 11 | 2 | 0.182 | 0.222 | -1.504 |
| Asian | 74.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 80.537 | 54 | 4 | 0.074 | 0.080 | -2.526 | |
| Hispanic/Latino | 74.000 | 5 | 3 | 0.600 | 1.500 | 0.405 | |
| Other/Multiracial | 68.000 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| Unavailable/Unknown | 77.000 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| 12 | African Amer/Black | 81.000 | 12 | 0 | 0.000 | 0.000 | -Inf |
| Asian | 73.000 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 83.507 | 71 | 10 | 0.141 | 0.164 | -1.808 | |
| Hispanic/Latino | 73.333 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 84.000 | 2 | 2 | 1.000 | Inf | Inf | |
| Unavailable/Unknown | 79.000 | 2 | 1 | 0.500 | 1.000 | 0.000 | |
| 13 | African Amer/Black | 76.000 | 2 | 0 | 0.000 | 0.000 | -Inf |
| Caucasian/White | 84.806 | 31 | 10 | 0.323 | 0.476 | -0.742 | |
| Unavailable/Unknown | 85.000 | 1 | 1 | 1.000 | Inf | Inf | |
| 14 | African Amer/Black | 82.500 | 4 | 0 | 0.000 | 0.000 | -Inf |
| Caucasian/White | 85.692 | 13 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 82.000 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| 15 | Asian | 66.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| Caucasian/White | 88.000 | 6 | 0 | 0.000 | 0.000 | -Inf | |
| 16 | Caucasian/White | 79.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| 17 | Caucasian/White | 83.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| CCI Score | Insurance | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|---|
| 0 | MCARE_MCAID | 40.684 | 19 | 4 | 0.211 | 0.267 | -1.322 |
| NO_MCARE_MCAID | 41.981 | 52 | 6 | 0.115 | 0.130 | -2.037 | |
| 1 | MCARE_MCAID | 54.014 | 73 | 9 | 0.123 | 0.141 | -1.962 |
| NO_MCARE_MCAID | 53.676 | 170 | 19 | 0.112 | 0.126 | -2.073 | |
| 2 | MCARE_MCAID | 64.725 | 491 | 79 | 0.161 | 0.192 | -1.652 |
| NO_MCARE_MCAID | 61.234 | 385 | 51 | 0.132 | 0.153 | -1.879 | |
| 3 | MCARE_MCAID | 73.021 | 1445 | 235 | 0.163 | 0.194 | -1.639 |
| NO_MCARE_MCAID | 66.815 | 503 | 66 | 0.131 | 0.151 | -1.890 | |
| 4 | MCARE_MCAID | 83.836 | 3455 | 548 | 0.159 | 0.189 | -1.669 |
| NO_MCARE_MCAID | 75.215 | 594 | 93 | 0.157 | 0.186 | -1.684 | |
| 5 | MCARE_MCAID | 82.872 | 2302 | 383 | 0.166 | 0.200 | -1.612 |
| NO_MCARE_MCAID | 75.920 | 336 | 44 | 0.131 | 0.151 | -1.893 | |
| 6 | MCARE_MCAID | 84.299 | 1568 | 255 | 0.163 | 0.194 | -1.639 |
| NO_MCARE_MCAID | 78.668 | 274 | 45 | 0.164 | 0.197 | -1.627 | |
| 7 | MCARE_MCAID | 85.226 | 867 | 118 | 0.136 | 0.158 | -1.848 |
| NO_MCARE_MCAID | 77.038 | 132 | 23 | 0.174 | 0.211 | -1.556 | |
| 8 | MCARE_MCAID | 84.634 | 462 | 83 | 0.180 | 0.219 | -1.519 |
| NO_MCARE_MCAID | 77.309 | 55 | 7 | 0.127 | 0.146 | -1.925 | |
| 9 | MCARE_MCAID | 84.252 | 214 | 28 | 0.131 | 0.151 | -1.894 |
| NO_MCARE_MCAID | 76.556 | 36 | 5 | 0.139 | 0.161 | -1.825 | |
| 10 | MCARE_MCAID | 82.919 | 136 | 19 | 0.140 | 0.162 | -1.818 |
| NO_MCARE_MCAID | 78.083 | 12 | 2 | 0.167 | 0.200 | -1.609 | |
| 11 | MCARE_MCAID | 80.227 | 66 | 6 | 0.091 | 0.100 | -2.303 |
| NO_MCARE_MCAID | 73.222 | 9 | 3 | 0.333 | 0.500 | -0.693 | |
| 12 | MCARE_MCAID | 82.595 | 79 | 12 | 0.152 | 0.179 | -1.720 |
| NO_MCARE_MCAID | 82.154 | 13 | 1 | 0.077 | 0.083 | -2.485 | |
| 13 | MCARE_MCAID | 85.452 | 31 | 10 | 0.323 | 0.476 | -0.742 |
| NO_MCARE_MCAID | 72.333 | 3 | 1 | 0.333 | 0.500 | -0.693 | |
| 14 | MCARE_MCAID | 84.765 | 17 | 0 | 0.000 | 0.000 | -Inf |
| NO_MCARE_MCAID | 83.500 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| 15 | MCARE_MCAID | 88.000 | 6 | 0 | 0.000 | 0.000 | -Inf |
| NO_MCARE_MCAID | 66.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| 16 | MCARE_MCAID | 79.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| 17 | MCARE_MCAID | 83.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| LACE Score | Gender | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|---|
| 2 | Female | 46.750 | 4 | 0 | 0.000 | 0.000 | -Inf |
| Male | 25.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| 3 | Female | 48.200 | 5 | 1 | 0.200 | 0.250 | -1.386 |
| 4 | Female | 56.484 | 31 | 1 | 0.032 | 0.033 | -3.401 |
| Male | 59.154 | 13 | 0 | 0.000 | 0.000 | -Inf | |
| 5 | Female | 62.148 | 61 | 2 | 0.033 | 0.034 | -3.384 |
| Male | 60.872 | 39 | 3 | 0.077 | 0.083 | -2.485 | |
| 6 | Female | 67.962 | 159 | 8 | 0.050 | 0.053 | -2.938 |
| Male | 66.787 | 80 | 9 | 0.112 | 0.127 | -2.065 | |
| 7 | Female | 71.298 | 242 | 25 | 0.103 | 0.115 | -2.161 |
| Male | 66.821 | 117 | 19 | 0.162 | 0.194 | -1.641 | |
| 8 | Female | 75.782 | 413 | 40 | 0.097 | 0.107 | -2.233 |
| Male | 73.808 | 239 | 36 | 0.151 | 0.177 | -1.730 | |
| 9 | Female | 78.053 | 719 | 69 | 0.096 | 0.106 | -2.243 |
| Male | 77.402 | 396 | 60 | 0.152 | 0.179 | -1.723 | |
| 10 | Female | 77.158 | 931 | 126 | 0.135 | 0.157 | -1.855 |
| Male | 77.343 | 531 | 84 | 0.158 | 0.188 | -1.672 | |
| 11 | Female | 79.351 | 1106 | 114 | 0.103 | 0.115 | -2.164 |
| Male | 76.548 | 577 | 89 | 0.154 | 0.182 | -1.702 | |
| 12 | Female | 82.776 | 1970 | 226 | 0.115 | 0.130 | -2.043 |
| Male | 81.099 | 1073 | 176 | 0.164 | 0.196 | -1.629 | |
| 13 | Female | 82.224 | 1838 | 292 | 0.159 | 0.189 | -1.667 |
| Male | 80.581 | 1159 | 225 | 0.194 | 0.241 | -1.423 | |
| 14 | Female | 81.462 | 344 | 69 | 0.201 | 0.251 | -1.383 |
| Male | 79.619 | 252 | 62 | 0.246 | 0.326 | -1.120 | |
| 15 | Female | 80.468 | 656 | 162 | 0.247 | 0.328 | -1.115 |
| Male | 79.053 | 547 | 151 | 0.276 | 0.381 | -0.964 | |
| 16 | Female | 79.297 | 128 | 34 | 0.266 | 0.362 | -1.017 |
| Male | 80.887 | 106 | 46 | 0.434 | 0.767 | -0.266 | |
| 17 | Female | 77.692 | 26 | 12 | 0.462 | 0.857 | -0.154 |
| Male | 77.074 | 27 | 9 | 0.333 | 0.500 | -0.693 | |
| 18 | Female | 80.500 | 2 | 1 | 0.500 | 1.000 | 0.000 |
| Male | 77.778 | 9 | 0 | 0.000 | 0.000 | -Inf | |
| 19 | Female | 78.000 | 4 | 2 | 0.500 | 1.000 | 0.000 |
| Male | 83.600 | 5 | 2 | 0.400 | 0.667 | -0.405 |
| LACE Score | Race/Ethnicity | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|---|
| 2 | African Amer/Black | 39.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| Caucasian/White | 56.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 39.000 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| 3 | African Amer/Black | 51.000 | 2 | 1 | 0.500 | 1.000 | 0.000 |
| Caucasian/White | 55.500 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 28.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| 4 | African Amer/Black | 50.600 | 5 | 1 | 0.200 | 0.250 | -1.386 |
| Asian | 65.500 | 4 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 57.714 | 28 | 0 | 0.000 | 0.000 | -Inf | |
| Hispanic/Latino | 52.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 53.000 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| Unavailable/Unknown | 59.333 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| 5 | African Amer/Black | 58.769 | 13 | 2 | 0.154 | 0.182 | -1.705 |
| Asian | 58.714 | 7 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 62.864 | 66 | 1 | 0.015 | 0.015 | -4.174 | |
| Hispanic/Latino | 56.000 | 6 | 1 | 0.167 | 0.200 | -1.609 | |
| Other/Multiracial | 57.400 | 5 | 0 | 0.000 | 0.000 | -Inf | |
| Unavailable/Unknown | 72.667 | 3 | 1 | 0.333 | 0.500 | -0.693 | |
| 6 | African Amer/Black | 62.784 | 37 | 5 | 0.135 | 0.156 | -1.856 |
| Asian | 68.182 | 11 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 68.819 | 166 | 9 | 0.054 | 0.057 | -2.859 | |
| Hispanic/Latino | 66.286 | 14 | 1 | 0.071 | 0.077 | -2.565 | |
| Other/Multiracial | 64.429 | 7 | 1 | 0.143 | 0.167 | -1.792 | |
| Unavailable/Unknown | 68.250 | 4 | 1 | 0.250 | 0.333 | -1.099 | |
| 7 | African Amer/Black | 65.033 | 60 | 8 | 0.133 | 0.154 | -1.872 |
| Asian | 69.611 | 18 | 2 | 0.111 | 0.125 | -2.079 | |
| Caucasian/White | 70.992 | 250 | 33 | 0.132 | 0.152 | -1.883 | |
| Hispanic/Latino | 67.083 | 12 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 70.750 | 12 | 1 | 0.083 | 0.091 | -2.398 | |
| Unavailable/Unknown | 73.571 | 7 | 0 | 0.000 | 0.000 | -Inf | |
| 8 | African Amer/Black | 68.493 | 67 | 3 | 0.045 | 0.047 | -3.060 |
| Asian | 70.865 | 37 | 3 | 0.081 | 0.088 | -2.428 | |
| Caucasian/White | 77.197 | 472 | 57 | 0.121 | 0.137 | -1.985 | |
| Hispanic/Latino | 66.897 | 29 | 5 | 0.172 | 0.208 | -1.569 | |
| Other/Multiracial | 70.667 | 33 | 6 | 0.182 | 0.222 | -1.504 | |
| Unavailable/Unknown | 72.714 | 14 | 2 | 0.143 | 0.167 | -1.792 | |
| 9 | African Amer/Black | 69.639 | 108 | 16 | 0.148 | 0.174 | -1.749 |
| Asian | 76.712 | 52 | 5 | 0.096 | 0.106 | -2.241 | |
| Caucasian/White | 79.534 | 839 | 98 | 0.117 | 0.132 | -2.023 | |
| Hispanic/Latino | 68.656 | 32 | 2 | 0.062 | 0.067 | -2.708 | |
| Other/Multiracial | 74.278 | 54 | 6 | 0.111 | 0.125 | -2.079 | |
| Unavailable/Unknown | 77.467 | 30 | 2 | 0.067 | 0.071 | -2.639 | |
| 10 | African Amer/Black | 69.589 | 190 | 28 | 0.147 | 0.173 | -1.755 |
| Asian | 72.017 | 60 | 5 | 0.083 | 0.091 | -2.398 | |
| Caucasian/White | 79.258 | 1035 | 157 | 0.152 | 0.179 | -1.721 | |
| Hispanic/Latino | 72.632 | 68 | 6 | 0.088 | 0.097 | -2.335 | |
| Other/Multiracial | 76.024 | 85 | 8 | 0.094 | 0.104 | -2.264 | |
| Unavailable/Unknown | 80.292 | 24 | 6 | 0.250 | 0.333 | -1.099 | |
| 11 | African Amer/Black | 72.246 | 187 | 28 | 0.150 | 0.176 | -1.737 |
| Asian | 73.476 | 63 | 11 | 0.175 | 0.212 | -1.553 | |
| Caucasian/White | 80.053 | 1288 | 148 | 0.115 | 0.130 | -2.042 | |
| Hispanic/Latino | 73.186 | 43 | 7 | 0.163 | 0.194 | -1.638 | |
| Other/Multiracial | 72.827 | 75 | 4 | 0.053 | 0.056 | -2.876 | |
| Unavailable/Unknown | 76.815 | 27 | 5 | 0.185 | 0.227 | -1.482 | |
| 12 | African Amer/Black | 75.956 | 270 | 37 | 0.137 | 0.159 | -1.840 |
| Asian | 78.198 | 106 | 13 | 0.123 | 0.140 | -1.968 | |
| Caucasian/White | 83.314 | 2379 | 322 | 0.135 | 0.157 | -1.854 | |
| Hispanic/Latino | 78.671 | 82 | 5 | 0.061 | 0.065 | -2.734 | |
| Other/Multiracial | 80.463 | 149 | 13 | 0.087 | 0.096 | -2.348 | |
| Unavailable/Unknown | 81.544 | 57 | 12 | 0.211 | 0.267 | -1.322 | |
| 13 | African Amer/Black | 76.476 | 330 | 56 | 0.170 | 0.204 | -1.588 |
| Asian | 78.133 | 98 | 18 | 0.184 | 0.225 | -1.492 | |
| Caucasian/White | 82.706 | 2308 | 400 | 0.173 | 0.210 | -1.562 | |
| Hispanic/Latino | 78.420 | 100 | 14 | 0.140 | 0.163 | -1.815 | |
| Other/Multiracial | 80.227 | 110 | 16 | 0.145 | 0.170 | -1.771 | |
| Unavailable/Unknown | 79.882 | 51 | 13 | 0.255 | 0.342 | -1.073 | |
| 14 | African Amer/Black | 75.854 | 82 | 16 | 0.195 | 0.242 | -1.417 |
| Asian | 73.895 | 19 | 4 | 0.211 | 0.267 | -1.322 | |
| Caucasian/White | 81.878 | 417 | 95 | 0.228 | 0.295 | -1.221 | |
| Hispanic/Latino | 78.964 | 28 | 2 | 0.071 | 0.077 | -2.565 | |
| Other/Multiracial | 80.919 | 37 | 10 | 0.270 | 0.370 | -0.993 | |
| Unavailable/Unknown | 85.769 | 13 | 4 | 0.308 | 0.444 | -0.811 | |
| 15 | African Amer/Black | 76.783 | 166 | 44 | 0.265 | 0.361 | -1.020 |
| Asian | 77.465 | 43 | 6 | 0.140 | 0.162 | -1.819 | |
| Caucasian/White | 80.794 | 867 | 226 | 0.261 | 0.353 | -1.042 | |
| Hispanic/Latino | 75.455 | 44 | 8 | 0.182 | 0.222 | -1.504 | |
| Other/Multiracial | 78.683 | 60 | 22 | 0.367 | 0.579 | -0.547 | |
| Unavailable/Unknown | 81.000 | 23 | 7 | 0.304 | 0.438 | -0.827 | |
| 16 | African Amer/Black | 73.467 | 30 | 10 | 0.333 | 0.500 | -0.693 |
| Asian | 75.167 | 6 | 2 | 0.333 | 0.500 | -0.693 | |
| Caucasian/White | 81.606 | 170 | 59 | 0.347 | 0.532 | -0.632 | |
| Hispanic/Latino | 79.182 | 11 | 2 | 0.182 | 0.222 | -1.504 | |
| Other/Multiracial | 79.214 | 14 | 6 | 0.429 | 0.750 | -0.288 | |
| Unavailable/Unknown | 72.000 | 3 | 1 | 0.333 | 0.500 | -0.693 | |
| 17 | African Amer/Black | 76.286 | 14 | 8 | 0.571 | 1.333 | 0.288 |
| Caucasian/White | 79.971 | 34 | 11 | 0.324 | 0.478 | -0.738 | |
| Hispanic/Latino | 67.500 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 59.667 | 3 | 2 | 0.667 | 2.000 | 0.693 | |
| 18 | African Amer/Black | 77.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| Asian | 64.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 80.000 | 9 | 1 | 0.111 | 0.125 | -2.079 | |
| 19 | African Amer/Black | 67.000 | 2 | 1 | 0.500 | 1.000 | 0.000 |
| Caucasian/White | 84.333 | 6 | 3 | 0.500 | 1.000 | 0.000 | |
| Hispanic/Latino | 90.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| LACE Score | Insurance | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|---|
| 2 | NO_MCARE_MCAID | 42.400 | 5 | 0 | 0.000 | 0.000 | -Inf |
| 3 | MCARE_MCAID | 49.500 | 2 | 1 | 0.500 | 1.000 | 0.000 |
| NO_MCARE_MCAID | 47.333 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| 4 | MCARE_MCAID | 63.154 | 13 | 0 | 0.000 | 0.000 | -Inf |
| NO_MCARE_MCAID | 54.806 | 31 | 1 | 0.032 | 0.033 | -3.401 | |
| 5 | MCARE_MCAID | 65.851 | 47 | 2 | 0.043 | 0.044 | -3.114 |
| NO_MCARE_MCAID | 57.925 | 53 | 3 | 0.057 | 0.060 | -2.813 | |
| 6 | MCARE_MCAID | 71.081 | 160 | 12 | 0.075 | 0.081 | -2.512 |
| NO_MCARE_MCAID | 60.456 | 79 | 5 | 0.063 | 0.068 | -2.695 | |
| 7 | MCARE_MCAID | 73.233 | 232 | 32 | 0.138 | 0.160 | -1.833 |
| NO_MCARE_MCAID | 63.638 | 127 | 12 | 0.094 | 0.104 | -2.260 | |
| 8 | MCARE_MCAID | 77.881 | 512 | 63 | 0.123 | 0.140 | -1.964 |
| NO_MCARE_MCAID | 64.736 | 140 | 13 | 0.093 | 0.102 | -2.279 | |
| 9 | MCARE_MCAID | 80.421 | 878 | 111 | 0.126 | 0.145 | -1.933 |
| NO_MCARE_MCAID | 68.190 | 237 | 18 | 0.076 | 0.082 | -2.499 | |
| 10 | MCARE_MCAID | 79.736 | 1143 | 171 | 0.150 | 0.176 | -1.738 |
| NO_MCARE_MCAID | 68.229 | 319 | 39 | 0.122 | 0.139 | -1.971 | |
| 11 | MCARE_MCAID | 80.267 | 1398 | 172 | 0.123 | 0.140 | -1.964 |
| NO_MCARE_MCAID | 69.182 | 285 | 31 | 0.109 | 0.122 | -2.103 | |
| 12 | MCARE_MCAID | 83.816 | 2585 | 345 | 0.133 | 0.154 | -1.871 |
| NO_MCARE_MCAID | 72.978 | 458 | 57 | 0.124 | 0.142 | -1.951 | |
| 13 | MCARE_MCAID | 82.802 | 2527 | 422 | 0.167 | 0.200 | -1.607 |
| NO_MCARE_MCAID | 75.062 | 470 | 95 | 0.202 | 0.253 | -1.373 | |
| 14 | MCARE_MCAID | 82.099 | 517 | 116 | 0.224 | 0.289 | -1.240 |
| NO_MCARE_MCAID | 71.418 | 79 | 15 | 0.190 | 0.234 | -1.451 | |
| 15 | MCARE_MCAID | 81.228 | 978 | 257 | 0.263 | 0.356 | -1.032 |
| NO_MCARE_MCAID | 73.724 | 225 | 56 | 0.249 | 0.331 | -1.105 | |
| 16 | MCARE_MCAID | 81.346 | 191 | 67 | 0.351 | 0.540 | -0.616 |
| NO_MCARE_MCAID | 74.116 | 43 | 13 | 0.302 | 0.433 | -0.836 | |
| 17 | MCARE_MCAID | 78.056 | 36 | 15 | 0.417 | 0.714 | -0.336 |
| NO_MCARE_MCAID | 75.941 | 17 | 6 | 0.353 | 0.545 | -0.606 | |
| 18 | MCARE_MCAID | 82.125 | 8 | 1 | 0.125 | 0.143 | -1.946 |
| NO_MCARE_MCAID | 68.000 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| 19 | MCARE_MCAID | 84.667 | 6 | 2 | 0.333 | 0.500 | -0.693 |
| NO_MCARE_MCAID | 74.000 | 3 | 2 | 0.667 | 2.000 | 0.693 |
| HOSP Score | Gender | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|---|
| 0 | Female | 80.000 | 66 | 2 | 0.030 | 0.031 | -3.466 |
| Male | 75.700 | 20 | 1 | 0.050 | 0.053 | -2.944 | |
| 1 | Female | 78.638 | 852 | 47 | 0.055 | 0.058 | -2.841 |
| Male | 78.341 | 346 | 33 | 0.095 | 0.105 | -2.250 | |
| 2 | Female | 79.922 | 1442 | 103 | 0.071 | 0.077 | -2.565 |
| Male | 78.459 | 603 | 67 | 0.111 | 0.125 | -2.079 | |
| 3 | Female | 80.388 | 1617 | 207 | 0.128 | 0.147 | -1.919 |
| Male | 79.168 | 961 | 171 | 0.178 | 0.216 | -1.530 | |
| 4 | Female | 80.746 | 2419 | 334 | 0.138 | 0.160 | -1.831 |
| Male | 78.941 | 1515 | 264 | 0.174 | 0.211 | -1.556 | |
| 5 | Female | 79.269 | 925 | 165 | 0.178 | 0.217 | -1.527 |
| Male | 78.386 | 660 | 145 | 0.220 | 0.282 | -1.267 | |
| 6 | Female | 79.046 | 849 | 187 | 0.220 | 0.282 | -1.264 |
| Male | 77.422 | 683 | 170 | 0.249 | 0.331 | -1.104 | |
| 7 | Female | 77.465 | 226 | 61 | 0.270 | 0.370 | -0.995 |
| Male | 77.201 | 164 | 43 | 0.262 | 0.355 | -1.035 | |
| 8 | Female | 74.656 | 151 | 47 | 0.311 | 0.452 | -0.794 |
| Male | 76.241 | 137 | 45 | 0.328 | 0.489 | -0.715 | |
| 9 | Female | 71.824 | 68 | 25 | 0.368 | 0.581 | -0.542 |
| Male | 74.375 | 56 | 22 | 0.393 | 0.647 | -0.435 | |
| 10 | Female | 74.385 | 13 | 4 | 0.308 | 0.444 | -0.811 |
| Male | 69.467 | 15 | 5 | 0.333 | 0.500 | -0.693 | |
| 11 | Female | 69.333 | 9 | 2 | 0.222 | 0.286 | -1.253 |
| Male | 74.091 | 11 | 5 | 0.455 | 0.833 | -0.182 | |
| 12 | Female | 82.500 | 2 | 0 | 0.000 | 0.000 | -Inf |
| HOSP Score | Race/Ethnicity | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|---|
| 0 | African Amer/Black | 68.857 | 7 | 0 | 0.000 | 0.000 | -Inf |
| Asian | 78.500 | 8 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 81.127 | 63 | 3 | 0.048 | 0.050 | -2.996 | |
| Hispanic/Latino | 71.667 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 64.667 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| Unavailable/Unknown | 82.000 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| 1 | African Amer/Black | 71.471 | 102 | 7 | 0.069 | 0.074 | -2.608 |
| Asian | 76.419 | 43 | 4 | 0.093 | 0.103 | -2.277 | |
| Caucasian/White | 79.919 | 939 | 56 | 0.060 | 0.063 | -2.758 | |
| Hispanic/Latino | 72.703 | 37 | 2 | 0.054 | 0.057 | -2.862 | |
| Other/Multiracial | 74.596 | 52 | 7 | 0.135 | 0.156 | -1.861 | |
| Unavailable/Unknown | 76.680 | 25 | 4 | 0.160 | 0.190 | -1.658 | |
| 2 | African Amer/Black | 72.815 | 189 | 13 | 0.069 | 0.074 | -2.606 |
| Asian | 76.269 | 93 | 5 | 0.054 | 0.057 | -2.868 | |
| Caucasian/White | 80.897 | 1577 | 140 | 0.089 | 0.097 | -2.329 | |
| Hispanic/Latino | 72.708 | 65 | 5 | 0.077 | 0.083 | -2.485 | |
| Other/Multiracial | 76.782 | 87 | 4 | 0.046 | 0.048 | -3.033 | |
| Unavailable/Unknown | 80.118 | 34 | 3 | 0.088 | 0.097 | -2.335 | |
| 3 | African Amer/Black | 74.405 | 259 | 35 | 0.135 | 0.156 | -1.856 |
| Asian | 76.348 | 92 | 18 | 0.196 | 0.243 | -1.414 | |
| Caucasian/White | 81.180 | 1964 | 291 | 0.148 | 0.174 | -1.749 | |
| Hispanic/Latino | 74.867 | 90 | 10 | 0.111 | 0.125 | -2.079 | |
| Other/Multiracial | 78.620 | 129 | 14 | 0.109 | 0.122 | -2.106 | |
| Unavailable/Unknown | 78.523 | 44 | 10 | 0.227 | 0.294 | -1.224 | |
| 4 | African Amer/Black | 73.988 | 424 | 69 | 0.163 | 0.194 | -1.638 |
| Asian | 74.164 | 152 | 20 | 0.132 | 0.152 | -1.887 | |
| Caucasian/White | 81.576 | 2969 | 460 | 0.155 | 0.183 | -1.696 | |
| Hispanic/Latino | 75.770 | 126 | 10 | 0.079 | 0.086 | -2.451 | |
| Other/Multiracial | 77.072 | 194 | 27 | 0.139 | 0.162 | -1.822 | |
| Unavailable/Unknown | 80.826 | 69 | 12 | 0.174 | 0.211 | -1.558 | |
| 5 | African Amer/Black | 73.370 | 219 | 40 | 0.183 | 0.223 | -1.499 |
| Asian | 74.840 | 50 | 8 | 0.160 | 0.190 | -1.658 | |
| Caucasian/White | 80.475 | 1158 | 232 | 0.200 | 0.251 | -1.384 | |
| Hispanic/Latino | 74.948 | 58 | 12 | 0.207 | 0.261 | -1.344 | |
| Other/Multiracial | 77.333 | 72 | 11 | 0.153 | 0.180 | -1.713 | |
| Unavailable/Unknown | 76.571 | 28 | 7 | 0.250 | 0.333 | -1.099 | |
| 6 | African Amer/Black | 72.956 | 225 | 48 | 0.213 | 0.271 | -1.305 |
| Asian | 74.190 | 63 | 11 | 0.175 | 0.212 | -1.553 | |
| Caucasian/White | 79.873 | 1083 | 259 | 0.239 | 0.314 | -1.157 | |
| Hispanic/Latino | 75.037 | 54 | 9 | 0.167 | 0.200 | -1.609 | |
| Other/Multiracial | 77.603 | 73 | 19 | 0.260 | 0.352 | -1.045 | |
| Unavailable/Unknown | 78.824 | 34 | 11 | 0.324 | 0.478 | -0.738 | |
| 7 | African Amer/Black | 71.172 | 58 | 18 | 0.310 | 0.450 | -0.799 |
| Asian | 73.692 | 13 | 3 | 0.231 | 0.300 | -1.204 | |
| Caucasian/White | 79.707 | 270 | 70 | 0.259 | 0.350 | -1.050 | |
| Hispanic/Latino | 72.217 | 23 | 3 | 0.130 | 0.150 | -1.897 | |
| Other/Multiracial | 72.412 | 17 | 6 | 0.353 | 0.545 | -0.606 | |
| Unavailable/Unknown | 74.333 | 9 | 4 | 0.444 | 0.800 | -0.223 | |
| 8 | African Amer/Black | 70.558 | 43 | 15 | 0.349 | 0.536 | -0.624 |
| Asian | 74.667 | 6 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 76.751 | 205 | 70 | 0.341 | 0.519 | -0.657 | |
| Hispanic/Latino | 74.545 | 11 | 1 | 0.091 | 0.100 | -2.303 | |
| Other/Multiracial | 68.769 | 13 | 3 | 0.231 | 0.300 | -1.204 | |
| Unavailable/Unknown | 78.800 | 10 | 3 | 0.300 | 0.429 | -0.847 | |
| 9 | African Amer/Black | 66.143 | 28 | 16 | 0.571 | 1.333 | 0.288 |
| Asian | 68.333 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 75.188 | 80 | 28 | 0.350 | 0.538 | -0.619 | |
| Hispanic/Latino | 88.000 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 69.125 | 8 | 3 | 0.375 | 0.600 | -0.511 | |
| Unavailable/Unknown | 82.667 | 3 | 0 | 0.000 | 0.000 | -Inf | |
| 10 | African Amer/Black | 76.429 | 7 | 1 | 0.143 | 0.167 | -1.792 |
| Asian | 51.000 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| Caucasian/White | 71.333 | 15 | 6 | 0.400 | 0.667 | -0.405 | |
| Hispanic/Latino | 82.000 | 2 | 1 | 0.500 | 1.000 | 0.000 | |
| Other/Multiracial | 61.000 | 1 | 1 | 1.000 | Inf | Inf | |
| Unavailable/Unknown | 77.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| 11 | African Amer/Black | 52.750 | 4 | 2 | 0.500 | 1.000 | 0.000 |
| Caucasian/White | 78.769 | 13 | 5 | 0.385 | 0.625 | -0.470 | |
| Hispanic/Latino | 64.000 | 2 | 0 | 0.000 | 0.000 | -Inf | |
| Other/Multiracial | 76.000 | 1 | 0 | 0.000 | 0.000 | -Inf | |
| 12 | Caucasian/White | 85.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| Other/Multiracial | 80.000 | 1 | 0 | 0.000 | 0.000 | -Inf |
| HOSP Score | Insurance | Mean Age | N | Readmit No. | Readmit Prop | Readmit Odds | Readmit Logit |
|---|---|---|---|---|---|---|---|
| 0 | MCARE_MCAID | 82.167 | 72 | 3 | 0.042 | 0.043 | -3.135 |
| NO_MCARE_MCAID | 62.714 | 14 | 0 | 0.000 | 0.000 | -Inf | |
| 1 | MCARE_MCAID | 81.140 | 972 | 71 | 0.073 | 0.079 | -2.541 |
| NO_MCARE_MCAID | 67.425 | 226 | 9 | 0.040 | 0.041 | -3.183 | |
| 2 | MCARE_MCAID | 81.553 | 1705 | 149 | 0.087 | 0.096 | -2.346 |
| NO_MCARE_MCAID | 69.150 | 340 | 21 | 0.062 | 0.066 | -2.721 | |
| 3 | MCARE_MCAID | 81.968 | 2115 | 319 | 0.151 | 0.178 | -1.728 |
| NO_MCARE_MCAID | 70.637 | 463 | 59 | 0.127 | 0.146 | -1.924 | |
| 4 | MCARE_MCAID | 82.120 | 3208 | 498 | 0.155 | 0.184 | -1.694 |
| NO_MCARE_MCAID | 70.905 | 726 | 100 | 0.138 | 0.160 | -1.834 | |
| 5 | MCARE_MCAID | 81.006 | 1267 | 246 | 0.194 | 0.241 | -1.423 |
| NO_MCARE_MCAID | 70.519 | 318 | 64 | 0.201 | 0.252 | -1.378 | |
| 6 | MCARE_MCAID | 80.067 | 1235 | 299 | 0.242 | 0.319 | -1.141 |
| NO_MCARE_MCAID | 71.064 | 297 | 58 | 0.195 | 0.243 | -1.416 | |
| 7 | MCARE_MCAID | 79.397 | 307 | 81 | 0.264 | 0.358 | -1.026 |
| NO_MCARE_MCAID | 69.795 | 83 | 23 | 0.277 | 0.383 | -0.959 | |
| 8 | MCARE_MCAID | 77.447 | 226 | 77 | 0.341 | 0.517 | -0.660 |
| NO_MCARE_MCAID | 67.984 | 62 | 15 | 0.242 | 0.319 | -1.142 | |
| 9 | MCARE_MCAID | 75.382 | 89 | 34 | 0.382 | 0.618 | -0.481 |
| NO_MCARE_MCAID | 66.857 | 35 | 13 | 0.371 | 0.591 | -0.526 | |
| 10 | MCARE_MCAID | 75.158 | 19 | 7 | 0.368 | 0.583 | -0.539 |
| NO_MCARE_MCAID | 64.556 | 9 | 2 | 0.222 | 0.286 | -1.253 | |
| 11 | MCARE_MCAID | 74.000 | 16 | 5 | 0.312 | 0.455 | -0.788 |
| NO_MCARE_MCAID | 63.750 | 4 | 2 | 0.500 | 1.000 | 0.000 | |
| 12 | MCARE_MCAID | 82.500 | 2 | 0 | 0.000 | 0.000 | -Inf |
Base CCI model: \(log(\frac{p}{1-p}) = b_0 + b_1*CCI\) :
##
## Call:
## glm(formula = cbind(n.Readmit, n - n.Readmit) ~ CCI, family = binomial(link = "logit"),
## data = readmit_cci_cut)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5701 -1.2023 -0.5058 0.5187 2.3662
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.70138 0.06099 -27.897 <2e-16 ***
## CCI 0.00285 0.01178 0.242 0.809
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 25.342 on 15 degrees of freedom
## Residual deviance: 25.284 on 14 degrees of freedom
## AIC: 110.25
##
## Number of Fisher Scoring iterations: 4
The results of the \(\chi^2_{14}\) goodness-of-fit test (p = 0.032) indicate significant evidence of lack of fit. This is likely due to the larger residuals for CCI values 13-14; could refit the model excluding this data which will result in better model fit, but it will not change the practical conclusion reached regarding the association between CCI score and risk of readmission.
##
## Call:
## glm(formula = cbind(n.Readmit, n - n.Readmit) ~ LACE, family = binomial(link = "logit"),
## data = readmit_lace)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.1637 -0.8923 0.7126 1.9487 2.7777
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.52140 0.13552 -25.98 <2e-16 ***
## LACE 0.15467 0.01101 14.04 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 276.245 on 17 degrees of freedom
## Residual deviance: 66.408 on 16 degrees of freedom
## AIC: 158.51
##
## Number of Fisher Scoring iterations: 4
##
## Call:
## glm(formula = cbind(n.Readmit, n - n.Readmit) ~ LACE, family = binomial(link = "logit"),
## data = readmit_lace_cut)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.1091 -0.6509 0.3533 1.5417 2.4112
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.44691 0.13355 -25.81 <2e-16 ***
## LACE 0.15332 0.01079 14.20 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 258.702 on 16 degrees of freedom
## Residual deviance: 44.266 on 15 degrees of freedom
## AIC: 128.67
##
## Number of Fisher Scoring iterations: 4
Removing the potential outlier does not improve goodness-of-fit, so rather than remove information we can use a quasibinomial distribution to increase the standard errors of the model estimates and account for the additional variation in the data. Model fitting with covariates may also resolve the issue of extra-binomial variation.
##
## Call:
## glm(formula = cbind(n.Readmit, n - n.Readmit) ~ HOSPITAL, family = binomial(link = "logit"),
## data = readmit_hos_cut)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4851 -1.4034 -0.4645 -0.1126 3.4206
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.70804 0.06081 -44.53 <2e-16 ***
## HOSPITAL 0.25061 0.01294 19.37 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 404.380 on 11 degrees of freedom
## Residual deviance: 26.824 on 10 degrees of freedom
## AIC: 101.73
##
## Number of Fisher Scoring iterations: 4